Mclandy

That's exactly right, you use a USB printer cable (Type A connector on one end, Type B on the other) to connect your Casio to a computer.  Get a good quality one if you need more than 10 feet of length.

To get the alternate bass notes on a chord, you need to configure the keyboard to be in either "Fingered 3" or "Full Range" chord modes.  See the fingering guide near the end of the manual.  Select the chord fingering mode by touching "Rhythm" on the MENU screen, then "Chord Input Type".  Note that if you haven't used these modes before, it might take a little practice to finger the chord properly, in order to get the bass note you want.

Der einfachste Weg, die Lautstärke der Begleitung relativ zu den Keyboard-Tönen einzustellen, besteht darin, die Taste "Funktion" zu drücken und nach links/rechts zu scrollen, bis Sie die Einstellung "Auto Accompaniment Volume" finden. Passen Sie das nach oben oder unten an, bis Sie mit der Balance zufrieden sind.

"Tune" as in "tuning a piano" - that is, making fine adjustments to the pitch of notes on the keyboard.  Most of the time you wouldn't touch this.  But if you are playing with other instruments or an audio file and the notes seem slightly "off", then you can use the Tune adjustments on the keyboard to raise or lower the pitch as needed.  Pages EN-37/38 in the manual.

Right.  On the X700, a few settings are preserved (Equalizer, Tuning, Registration Memory Freeze Target, Tap Rhythm Start, On-screen Keyboard, Display Contrast) over a power-off, but the rest, including Touch Response, apparently reset to defaults.

While Bluetooth latencies in the past have varied widely, some of the newer Bluetooth (5.0+) transmitters and headphones have technology that significantly reduces the latency.  For example, Qualcomm's Aptx-Low Latency (available at pretty reasonable prices now in headphones and transmitters) reduces the latency to below 40ms, which is about the limit that most people can actually distinguish.  I believe its primary purpose was for things like TV and gaming, where a timing difference between what you hear and the action/dialog on the screen can be a little distracting.  But in music terms, you can think of it as no more than the duration of a 64th note when playing 120BPM.  So while wired is still better, I'd say that Bluetooth is no longer out of the question for music instrument monitoring.

A while back, we mapped out all the note transpositions that are done for every  possible combination of the setting of the Chord Conversion Table, and the type of chord being played.  The table is available in the forum post at the link below.  These tables are quite detailed, and don't really explain in simple language terms what the "purpose" of each CCT setting is, but they do show exactly how chord notes get transposed. 
 
I will provide this one piece of advice, however - for most rhythms, I use the Bass 7th (for bass parts) and Chord 7th (for chord parts) in Variations/Fills, and Intro No Change for bass/chords in Intros and Endings.   For the Variations/Fills, if you record tracks using 7th chords (C,E,G,Bb), and use a Bass/Chord 7th CCT, then the 7th note (Bb) transposes to high C when playing a straight major/minor chord, stays at Bb when playing any 7th chord, and transposes to B when playing any Maj7 chord.  So it basically sounds good and full for any chord you play while using that rhythm.  The main problem (a big one) with Chord Basic is that it transposes C notes to Bb notes when you play a 7th chord, or to B if you play a Maj7 chord, so you lose your "root" note.  And all the other CCT settings are mostly for special cases, like if you are copying from some other original music sequence that was recorded using a minor chord or a "tension" chord (9, 11, 13 chords) or a non-chordal musical phrase.  90+% of the time, you just want the Bass/Chord 7th.
 
So here's where to find the detailed transposition table (spreadsheet):
 

Yes, it's exactly the same problem with Quantize in the Phrase Pad recording.  It makes it seem like random notes were added, but it's actually because the notes you do play get shifted in unexpected ways by the Quantize function.

I think you'll find that almost all of the Organ Tones on the CT-X5000 already have a rotary speaker effect built into them, based on the predefined DSPs associated with each tone.  You can modify the parameters on the Rotary DSP module in each tone by following the Tone Editing procedures outlined in the manual starting on page EN-71.  Navigate to the DSP section, find the Rotary (or Drive Rotary) DSP module in the DSP settings, and try tweaking some of the settings to adjust rotary type, speed, depth, and other characteristics (see manual pages EN-137/138 for all the parameters).  If you want to apply such effects to something other than an Organ tone, you can edit that other tone and select a DSP number matching one of the Organ tones, which will cause that organ tone's DSP effect (including rotary) to be applied to that other instrument.  Beyond that, you mostly have to experiment with the settings to get the sound you want.
 
Note: If you want to have the effect change while you are playing (like, for example, going from slow to fast rotary speed), you can do so by setting up the Modulation/Assignable button to change one of the DSP parameters on the fly.  See manual page EN-33.

I'd strongly second this approach, because I find that my "preferred initial setup" is definitely not the same as Casio's default settings.

To play alternate bass notes, you have to select the "Fingered On Bass" fingering mode.  Fingered 1 and 2 do not play alternate bass notes (except when such notes are included in the bass pattern).   In Fingered on Bass mode, the keyboard display does show the chord and root note (for example, C/G).  See page EN-49 and A3 in the manual.

Distortion is one of the options in the DSP functions, which is one group of available settings when editing a Tone (see page EN-75 in the manual).    It also depends on which preset DSP you select when editing the Tone, because not all DSPs have the distortion effect.  If you start with a tone that already includes a distortion DSP (most of the "crunch" and "distort" guitar sounds do), you can modify the parameters defined in the manual on page EN-141 to create different distortion sounds.  Or, you can start with any voice and select DSP #824, which is just straight distortion effect, or the DSP of one of those basic guitar sounds in the 125-160 range as a starting point, and then tune the parameters to your liking from there.  Other effects (DSP modules) that you might want to include, depending on what sound you want, are "Drive" and "Cabinet".
 
Here is a link to an earlier thread containing a document that shows which DSP modules are included in all of the different voices (on the CT-X5000, but many are the same on the 3000):
 

Glad to help.  It definitely gets easier the more you do it.  Have fun!